Time series are the common mathematical framework used to represent the world of economics and finance. Among time series, the first important classification can be done according to the spacing of data points in time. Regularly spaced time series are called homogeneous, irregularly spaced series are inhomogeneous. An example of a homogeneous time series is a series of daily data, where the data points are separated by one day (on a business time scale, which omits the weekends and holidays) .
In most references on time series analysis, the time series to be treated are restricted to the filed of homogeneous time series (see, e.g., Granger C. W. J. and Newbold P., 1977, Forecasting economic time series, Academic Press, London; Priestley M. B., 1989, Non-linear and non-stationary time series analysis, Academic Press, London; Hamilton J. D., 1994, Time Series Analysis, Princeton University Press, Princeton, N.J.) (hereinafter, respectively, Granger and Newbold, 1977; Priestley, 1989; Hamilton, 1994). This restriction induces numerous simplifications, both conceptually and computationally, and was justified before fast, inexpensive computers and high-frequency time series were available.
Current empirical research in finance is confronted with an ever-increasing amount of data, caused in part by increased computer power and communication speed. Many time series can be obtained at high frequency, often at market tick-by-tick frequency. These time series are inhomogeneous, since market ticks arrive at random times. Inhomogeneous time series by themselves are conceptually simple; the difficulty lies in efficiently extracting and computing information from them.